This research will be done primarily in Beijing China at Peking University in collaboration with Junni Zhang, Ph.D. as an extension of NIH grant # R01 HL62567. In the parent grant, we propose to develop a general statistical methodology for causal treatment analysis of the randomized encouragement design studies or randomized clinical trials with non-compliance. One additional issue in clinical trials with non-compliance we have not considered in the parent grant is 'truncation by death". Traditional approaches addressing this issue ignore the fact that the outcome after the truncation is neither "censored" nor "missing", but should be treated as being defined on an extended sample space. In this extension of the parent grant, we will discuss a newformulation for tackling this issue, where we call the outcome "truncated by death" because there is no hidden value of the outcome variable masked by the truncating event. We will further extend the framework to observational studies with possibly missing- data.